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Frankly, I'm at a point where I'm at a loss trying to figure out what your point is:

"The Naked Time" - Where is the line of dialogue that established that blasting out of orbit was still an option? The context of the episode suggests that by the time they finally got into the engineering control room their orbit had deterioted so much, that only warp power could save them from crashing.

"The Doomsday Machine" - Fine, deflector shields might have been knocked out by the same hit that took out the main energizers but that wasn't the issue:

(Another blast from the machine.) Spock looks up at a monitor of his science station, get's up and goes to Lt. Palmer's station
SPOCK: Sir, deflector shields are gone.
PALMER: (to Spock) Sir, Deck seven reports power failure in main energisers. Implementing emergency procedures. (another hit) Severe casualties reported on decks three and four. Damage control party sealing off inner hull rupture. Lt. Palmer's report could indicate the reason for their loss of deflector shields or a independent event.

SPOCK: It has ceased fire. We're being held in a tractor beam. We're being pulled inside, Commodore. You must veer off.
DECKER: Maintain phaser fire, helmsman.
SPOCK: We have lost warp power. If we don't break the tractor beam within sixty seconds, we never will.

This is the decisive part and information. Spock informs Decker they lost warp power. Where is the report, how does Spock know, especially where is the proof to pursuade Decker to veer off???

Decker is so pre-occupied with satisfying his Ahab Complex that Spock has to snap him out of it.
Lt. Palmer's audible report was "main energizer failure", the ship is now operating on battery power (it can still charge its phaser banks)but has been practically crippled. Instead of giving a lengthy explanation Spock highlights their biggest handicap (as a result of the main energizer failure) he assumes Commodore Decker, an experienced starship commander, to understand: "We have lost warp power".

Decker snaps out of it and understands, but now argues like a little child:

DECKER: But don't you understand? We've got to destroy it!
SPOCK: That, sir, is illogical. It is suicide. Attempted suicide would be proof that you are psychologically unfit for command. If you don't veer off, I shall relieve you on that basis.
DECKER: Veer off.
SPOCK: Emergency impulse power. (The ship is on battery power as it had been in "Mudd's Women" so it's fair to assume that "emergency" and "auxiliary" are the same).

Bob

__________________
"The first duty of every Starfleet officer is to the truth" Jean-Luc Picard
"We can't solve problems by using the same kind of thinking we used when we created them." Albert Einstein

Or is it that you are having problems imagining that "energizers" could refer to "fusion reactors"?

Bob

__________________
"The first duty of every Starfleet officer is to the truth" Jean-Luc Picard
"We can't solve problems by using the same kind of thinking we used when we created them." Albert Einstein

Frankly, I'm at a point where I'm at a loss trying to figure out what your point is:

It was to point out from your previous reply that impulse power wasn't available at any point after Riley took over. You had assumed that they had impulse and/or fusion power available to them when there was no evidence of that.

Also you made the assumption that impulse engines could not blast them out of orbit due to the deterioration of their orbit. That would make sense if they had impulse engines available, which again they did not. As far as we know, if the impulse engines were available, it could have been an option.

Robert Comsol wrote:

Later, Scotty was able to fix their impulse power: "Engineering to Bridge. Try your helm. You'll have enough (impulse) power to keep her stabilised."
But at this point their orbit had deteriorated to a point where it was only possible to "stabilise" but no longer to "blast out of the orbit".

It was imperative to use warp power which they finally managed. The problem was not the lack of fusion or impulse engine power but how to use the fusion power to heat up the antimatter and/or the engines to perform warp drive, IMHO.

Robert Comsol wrote:

"The Naked Time" - Where is the line of dialogue that established that blasting out of orbit was still an option?

There is no line of dialogue that said it was no longer an option. The last information we had was that either warp or impulse could save them.

Robert Comsol wrote:

The context of the episode suggests that by the time they finally got into the engineering control room their orbit had deterioted so much, that only warp power could save them from crashing.

I think we'll just have to disagree on that then as the context of the episode doesn't exclude the impulse engines as an option if they were available.

Robert Comsol wrote:

"The Doomsday Machine" - Fine, deflector shields might have been knocked out by the same hit that took out the main energizers but that wasn't the issue:
...Lt. Palmer's report could indicate the reason for their loss of deflector shields or a independent event.

I only commented on the deflectors because you listed the energizers as impacting the deflectors when it might not have been the case.

Which I guess goes back to the difference in opinion regarding fusion energy and dilithium crystals and/or energizers. Before this thread started, I assumed fusion reactors gave power to the impulse engines and were part of the auxiliary or emergency systems. But now digging into the episodes has opened up a can of worms where fusion reactor power and their availability is noticeably absent in the episodes they most could be used. Sigh. Anyway, carry on.